Numerical solutions of one-dimensional parabolic convection-diffusion problems arising in biology by the Laguerre collocation method
In this work, we present a numerical scheme for the approximate solutions of the one-dimensional parabolic convection-diffusion model problems. Diffusion models form a reasonable basis for studying insect and animal dispersal and invasion, which arise from the question of persistence of endangered s...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Bulgarian Academy of Sciences, Institute of Mathematics and Informatics
2017-06-01
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| Series: | Biomath |
| Online Access: | http://www.biomathforum.org/biomath/index.php/biomath/article/view/781 |
| _version_ | 1797727191805460480 |
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| author | Burcu Gürbüz Mehmet Sezer |
| author_facet | Burcu Gürbüz Mehmet Sezer |
| author_sort | Burcu Gürbüz |
| collection | DOAJ |
| description | In this work, we present a numerical scheme for the approximate solutions of the one-dimensional parabolic convection-diffusion model problems. Diffusion models form a reasonable basis for studying insect and animal dispersal and invasion, which arise from the question of persistence of endangered species, biodiversity, disease dynamics, multi-species competition so on. Convection diffusion problem is also a form of heat and mass transfer in biological models. The presented method is based on the Laguerre collocation method used for these problems of differential equations.
In fact, the approximate solution of the problem in the truncated Laguerre series form is obtained by this method. By substituting truncated Laguerre series solution into the problem and by using the matrix operations and the collocation points, the suggested scheme reduces the problem to a linear algebraic equation system. By solving this equation system, the unknown Laguerre coecients can be computed. The accuracy and the efficiency of the method is showed by numerical examples and the comparisons by the other methods. |
| first_indexed | 2024-03-12T10:56:19Z |
| format | Article |
| id | doaj.art-3eae82b6640646e59de2015586ef2363 |
| institution | Directory Open Access Journal |
| issn | 1314-684X 1314-7218 |
| language | English |
| last_indexed | 2024-03-12T10:56:19Z |
| publishDate | 2017-06-01 |
| publisher | Bulgarian Academy of Sciences, Institute of Mathematics and Informatics |
| record_format | Article |
| series | Biomath |
| spelling | doaj.art-3eae82b6640646e59de2015586ef23632023-09-02T06:20:05ZengBulgarian Academy of Sciences, Institute of Mathematics and InformaticsBiomath1314-684X1314-72182017-06-016110.11145/j.biomath.2017.06.047672Numerical solutions of one-dimensional parabolic convection-diffusion problems arising in biology by the Laguerre collocation methodBurcu Gürbüz0Mehmet Sezer1Celal Bayar UniversityManisa Celal Bayar UniversityIn this work, we present a numerical scheme for the approximate solutions of the one-dimensional parabolic convection-diffusion model problems. Diffusion models form a reasonable basis for studying insect and animal dispersal and invasion, which arise from the question of persistence of endangered species, biodiversity, disease dynamics, multi-species competition so on. Convection diffusion problem is also a form of heat and mass transfer in biological models. The presented method is based on the Laguerre collocation method used for these problems of differential equations. In fact, the approximate solution of the problem in the truncated Laguerre series form is obtained by this method. By substituting truncated Laguerre series solution into the problem and by using the matrix operations and the collocation points, the suggested scheme reduces the problem to a linear algebraic equation system. By solving this equation system, the unknown Laguerre coecients can be computed. The accuracy and the efficiency of the method is showed by numerical examples and the comparisons by the other methods.http://www.biomathforum.org/biomath/index.php/biomath/article/view/781 |
| spellingShingle | Burcu Gürbüz Mehmet Sezer Numerical solutions of one-dimensional parabolic convection-diffusion problems arising in biology by the Laguerre collocation method Biomath |
| title | Numerical solutions of one-dimensional parabolic convection-diffusion problems arising in biology by the Laguerre collocation method |
| title_full | Numerical solutions of one-dimensional parabolic convection-diffusion problems arising in biology by the Laguerre collocation method |
| title_fullStr | Numerical solutions of one-dimensional parabolic convection-diffusion problems arising in biology by the Laguerre collocation method |
| title_full_unstemmed | Numerical solutions of one-dimensional parabolic convection-diffusion problems arising in biology by the Laguerre collocation method |
| title_short | Numerical solutions of one-dimensional parabolic convection-diffusion problems arising in biology by the Laguerre collocation method |
| title_sort | numerical solutions of one dimensional parabolic convection diffusion problems arising in biology by the laguerre collocation method |
| url | http://www.biomathforum.org/biomath/index.php/biomath/article/view/781 |
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